Physics 7A -- Lecture 3 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg erbacher@physics.ucdavis.edu

Announcements Join this Class Session with your PRS clicker! (Credit begins today.) Quiz 2 is today! Lecture 1-2, DLMs 1-5. Must take it in your correct lecture time slot. Quiz 1 Rubric posted, and grading scale is linked. Check Physics 7 website frequently for calendar & Announcements. Turn off cell phones and pagers during lecture.

Energy Conserved ........   Emovement (KE) Espring Ethermal Ebond Enuclear Nuclear power plant There are many different forms of energy (energy systems): Steam engine  Emovement (KE)  Ethermal Ebond Espring Eelectric Egravity ........ Energy is converted from one form to another, but never created or destroyed!

Energy System Expressions Ethermal = C T = mcpT, Temperature is the indicator. Between phase changes, only thermal energy changes. Ebond = |m H|, m is the indicator. At a physical phase change, only the bond-energy system changes. H is the heat of the particular phase change. m is the amount that changed phase. In a chemical reaction, there are several bond energy changes corresponding to diff. molecular species (reactants or products). Here H is the heat of formation for a particular species. Ethermal Ebond

Energy Interaction Diagrams - Closed System Ea Eb Ec Conservation of Energy The total energy of a closed physical system must remain constant. So, the change of the energies of all energy systems associated with the physical system must sum to zero. Change in closed system energy = ∆Ea + ∆ Eb + ∆ Ec = 0

Energy Interaction Diagrams - Open System Energy added Energy removed Ea Eb Ec Conservation of Energy The change of the energies of all systems associated with an open physical system must sum to the net energy added or removed. Energy is added or removed as Heat or Work. Change in open system energy = ∆Ea + ∆ Eb + ∆ Ec = (Energy added) - (Energy removed) = Q + W.

Example for Open System Energy added = + 100 J Clicker! Ea Suppose we have a system where 100J of heat comes in from the outside. Joe claims that the only energy system that changes is Ea and that Ea is negative (Ea decreases). Can Joe be correct? Yes, its possible that he is correct. Yes, Joe is definitely correct. No way is Joe’s description correct.

Energy Interaction Diagrams Example: Melting Ice Ti= 0°C  Tf = room temperature Temperature Final gas Initial l-g coexist TBP s-l coexist liquid TMP solid Energy of substance

Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Process 2: Water at T=0ºC  Water at room temperature Process 1 Final / Process 2 Initial Temperature gas Process 1 Initial l-g coexist TBP liquid TMP s-l coexist Process 2 Final solid Energy of substance

Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice Ethermal Ebond ∆T=0 ∆Eth=0 Initial phase Solid, Final phase Liquid

Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice Ethermal Ebond Heat ∆T=0 ∆Eth=0 Initial phase Solid, Final phase Liquid

Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice Ethermal Ebond Heat ∆T=0 ∆Eth=0 Initial phase Solid, Final phase Liquid ∆Eth + ∆Ebond= Q+W ∆Ebond= Q

Energy Interaction Diagrams Example: Melting Ice Process 2: Water at T=0ºC  Water at room temperature Ice Ethermal Ebond Initial phase Liquid, Final phase Liquid

Energy Interaction Diagrams Example: Melting Ice Process 2: Water at T=0ºC  Water at room temperature Ice Ethermal Ebond Heat T ∆Eth + ∆Ebond= Q+W ∆Eth= Q Initial phase Liquid, Final phase Liquid ∆Ebond= 0

Energy Interaction Diagrams Example: Melting Ice Freezing (Water at T=0°C  Ice at T=0°C) Ice Ethermal Ebond Heat Initial phase Liquid, Final phase Solid ∆T=0 ∆Eth=0 NOTE: Heat is released when bonds are formed! (In general E is negative)

EIM Algebra Review For a closed system: (Is it clear why there’s no Q or W for a closed system?) For an open system: (Q and W can be positive or negative, as can Es.)

Three New Energy Systems

Examples: Mechanical Phenomena Emovement (KE) Espring Egravity Rear shock absorber and spring of BMW R75/5 Motorcycle

Kinetic Energy System (KE) Kinetic energy is simply Emoving. For translational energy, the indicator is speed; the faster an object moves, the more KE it has. There is a quantitative relationship between KE and speed. Also, it is proportional to the mass of the object: The direction of motion of the object is unimportant. KE Speed Baseball Work KEtrans = ½ m v2

Work KE Speed Remember this equation for an open system? You have worked a lot with Q, Heat. Now we introduce Work: Work: A transfer of energy that takes place from a physical system to another physical system due to an interaction that involves a Force. KE Speed Baseball Work 1) The pitcher’s hand “pushed” the baseball. 2) The pitcher’s hand exerted force on the baseball. 3) As a result, the baseball started moving (its KE increased).

May the Force Be With You! "an energy field, created by all living things, that surrounds us, penetrates us, and binds the galaxy together."

Force To be more precise, we need the concept of “Force” : “Push” or “Pull” An overall push (or pull!) in the direction the object is travelling has the effect of speeding it up. Consider a block being pushed by you on a level surface with no friction: 1) Block is already moving, you push in same direction: direction of Force Force as an agent of interaction of two objects, we are more interested in the interaction itself. Force is an agent of the interaction and the result of that interaction is different depending on the relative direction of the applied force and the object’s motion. Energy was transferred into the KE system of the block in forms of work KE Speed Work direction of travel

Force To be more precise, we need the concept of “Force” : “Push” or “Pull” An overall push (or pull!) in against the direction the object is travelling has the effect of slowing it down. Consider a block being pushed by you on a level surface with no friction: 2) Block is already moving, you push in opposite direction: Energy was transferred out of the KE system of the block in forms of work direction of Force KE Speed Work direction of travel

What’s force got to do with work? Transfer of energy into or out of a physical system by a force exerted by another physical system. The change in energy results from an interaction in which an object moves through a distance parallel to the force exerted on it. Work = Fparallel ∆x = F|| ∆x [Joule] = [Newton] [m]=[Nm]

Work Example How much energy was transferred to the KE system of the baseball in form of Work? Conservation of Energy says… ∆KE = Work ∆KE = KEfinal - KEinitial =1/2(m)(vf2) - 0 KE Speed Baseball Work (290 J, assume v=100mph=44m/s, m=0.3kg) Physics way of saying , Nolan Ryan pitched a ball at 100mph, The pitcher’s hand exerted 290 N amount of force on the baseball over a distance of 1m parallel to the ball’s velocity. Thus, the pitcher 290Joule amount of work on the ball, which is equal to the increase in the KE of the baseball. 100mph=160km/60min=160,000m/3600sec=44m/sec 290Joule 2. What about force? Work = F|| ∆ x= F|| (1m) F|| = 290 N

Properties of Forces Force is a vector quantity i.e. Forces have both magnitude and direction Force is the agent of interaction of TWO objects e.g. The pitcher’s hand and the baseball The two forces involved in an interaction are opposite and equal (Newton’s Third Law) Fhand on the baseball = - Fbaseball on the hand

Properties of Forces Force is a vector quantity i.e. Forces have both magnitude and direction Force is the agent of interaction of TWO objects e.g. The pitcher’s hand and the baseball The two forces involved in an interaction are opposite and equal (Newton’s Third Law) Contact force v. non contact force: Fgravitational

Pull Where did the energy go?? vf=0 vi=0 Work was done on the mass: Work = F||∆x Where did the energy go?? Pull m vf=0 What is the indicator of the object change? Temperature? Phase? Speed? ∆x PEgrav Height Work m vi=0 Conservation of Energy says… ∆PEgrav = Work = Fyou on mass ∆height= mg(hfinal - hinitial)

Potential Energy System (PE) Potential energy due to gravity: Eheight. (There are other types of PE, such as PE in a spring, or chemical PE.) For gravitational PE, the indicator is height; a higher object (with respect to something else) has more PEgravity. Can we show this? The quantitative relationship between PE and height: (g~10 m/s2 is the acceleration due to gravity on Earth.) PEgravity = mgh

Gravitational Potential Energy Gravitational potential energy-system exists for each pair of objects interacting by the gravitational force Usually, we focus on the gravitational potential energy due to the interaction between an object and the Earth. PEgravity = mgh ∆PEgravity depends on two quantities: the change in vertical distance that the object moved, and the mass of the object. Crumpled Paper KE Speed Note: we are neglecting the friction PEgrav Height

KE  PEgravity 1) You throw a ball to the height of the first floor window. 2) Now you want to throw a ball to the height of the 4th floor. Question: How much faster do you need to throw it? 2 times as fast Twice as fast Thrice as fast 4 times as fast 16 times as fast

Bowling Ball What is the height of the bowling ball after one full swing? Same (b) Higher (c) Lower

Bowling Ball When is the speed of the bowling ball maximum? c a b When is the speed of the bowling ball maximum? Starting point (b) When rope is vertical (c) After reaches point c.

Bowling Ball When is the PEgravity of the bowling ball maximum? c a b When is the PEgravity of the bowling ball maximum? Starting point (b) When rope is vertical (c) After reaches point c.

Conservation of Energy Consider a simple pendulum: At the height (peak) of the amplitude, the object is at rest. Egravity = mgh (define h above the low point) At the bottom of the motion, the object is moving quickly, and h=0. Etrans = ½ m v2 Conservation of Energy dictates that: PEgravity = KEtranslational mgh = ½ m v2 All of the PE goes into KE, and then back again!

Work  Kinetic Energy Only? Pull Work  Kinetic Energy Only? Mass is pulled part way up a well (like in FNT). This time work is done but there is no change in KE when v=0. Work entering or leaving does NOT automatically mean KE is increasing or decreasing. Similar to how heat entering or leaving does NOT automatically mean the temperature is changing. m v=0 m v=0

Bowling Ball Initial Final (Still in motion) KE Speed PEgrav Height

Bowling Ball Final Initial (In motion) KE Speed PEgrav Height

Bowling Ball Initial Final (Still in motion) KE Speed PEgrav Height

Potential Energy: Springs Springs contain energy when you stretch or compress them. We will use them a lot in Physics 7. The indicator is how much the spring is stretched or compressed, x, from its equilibrium (rest) state. k is a measure of the “stiffness” of the spring, with units [k] = kg/s2. x: Much easier to stretch a spring a little bit than a lot! PEspring = ½ kx2 x

PEvertical spring = ½ ky2 +C Mass-Spring Systems PEvertical spring = ½ ky2 +C k is a property of the spring only PEmass-spring does not depend on mass PE = 0 arbitrary

Mass-Spring Systems Is the KE (kinetic energy) of a mass-spring system a function of position? a) No, in this case the potential energy is a function of position. b) The kinetic energy can be treated as a function of position provided the system is closed. c) The kinetic energy can always be treated as a function of position in a mass-spring system. d) The kinetic energy can be treated as a function of position provided the system is open. e) Not enough information is given.

PEgravity = KEtranslational Kinetic Energy In any situation, KE is: Sometimes from the conservation of energy: we can express KE in terms of position (h, y, etc). KE can never be negative! KEtrans = ½ m v2 PEgravity = KEtranslational mgh = ½ m v2

Next Time: Potentials, and Particle Models of Matter